In his most stringent analysis, Polikoff found that only "27 percent to 38 percent of the textbooks' content is in perfect proportional agreement with the CCSS." Using a less rigorous definition of alignment that uses the standards as a reference and does not require proportional agreement, Polikoff found that between 63 percent and 79 percent of textbook content was aligned to the standards.

When flipping the analysis so that the textbooks were the reference, Polikoff found similar numbers, ranging from 70-76 percent alignment, though when ranking the textbooks this way, the order "is nearly the opposite of the rank ordering on the previously mentioned indices," wrote Polikoff in the paper. "That is, textbooks in which a larger proportion of the content comes from the standards are not necessarily the textbooks that cover the largest proportion of standards content."

In looking for the source of the misalignment, Polikoff found that the texts were approximately evenly split in misaligned topics and misaligned cognitive demand.

"The cognitive demand analysis indicates that each of the three CCSS-aligned textbooks and Saxon emphasizes memorization and procedures overwhelmingly," wrote Polikoff, with those categories representing between 88 and 93 percent of total content though the CCSS calls for just 60 percent of content to focus on those processes.

Conversely, although "almost one-third of the standards content calls for students to demonstrate understanding, just 7 percent to 12 percent of the textbooks' content is at this level," wrote Polikoff, and there is "essentially zero" content focused on the two top levels of cognitive demand despite their 11 percent representation in the standards.

Polikoff analyzed seven math textbooks designed for fourth-grade classrooms that are currently in use in Florida. Three of the textbooks analyzed are "Common-Core aligned," three were earlier versions of those books and the seventh is not specifically aligned with any standards. Florida was chosen because it is one of the only states that collects textbook adoption data by district and because it's "a statewide textbook adoption state and a large state that likely influences the content in textbooks nationwide," according to the paper.

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